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  • March 2022
  • Article
  • Annals of Applied Statistics

Estimating the Effectiveness of Permanent Price Reductions for Competing Products Using Multivariate Bayesian Structural Time Series Models

By: Fiammetta Menchetti and Iavor Bojinov
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Abstract

Researchers regularly use synthetic control methods for estimating causal effects when a sub-set of units receive a single persistent treatment, and the rest are unaffected by the change. In many applications, however, units not assigned to treatment are nevertheless impacted by the intervention because of cross-unit interactions. This paper extends the synthetic control methods to accommodate partial interference, allowing interactions within predefined groups, but not between them. Focusing on a class of causal estimands that capture the effect both on the treated and control units, we develop a multivariate Bayesian structural time series model for generating synthetic controls that would have occurred in the absence of an intervention enabling us to estimate our novel effects. In a simulation study, we explore our Bayesian procedure’s empirical properties and show that it achieves good frequentists coverage even when the model is misspecified. Our work is motivated by an analysis of a marketing campaign’s effectiveness by an Italian supermarket chain that permanently reduced the price of hundreds of store-brand products. We use our new methodology to make causal statements about the impact on sales of the affected store-brands and their direct competitors. Our proposed approach is implemented in the CausalMBSTS R package.

Keywords

Causal Inference; Partial Interference; Synthetic Controls; Bayesian Structural Time Series; Mathematical Methods

Citation

Menchetti, Fiammetta, and Iavor Bojinov. "Estimating the Effectiveness of Permanent Price Reductions for Competing Products Using Multivariate Bayesian Structural Time Series Models." Annals of Applied Statistics 16, no. 1 (March 2022): 414–435.
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About The Author

Iavor I. Bojinov

Technology and Operations Management
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  • Nailing Prediction: Experimental Evidence on the Value of Tools in Predictive Model Development By: Daniel Yue, Paul Hamilton and Iavor Bojinov
  • On Ramp to Crypto By: Iavor Bojinov, Michael Parzen and Paul Hamilton
  • A Causal Test of the Strength of Weak Ties By: Karthik Rajkumar, Guillaume Saint-Jacques, Iavor I. Bojinov, Erik Brynjolfsson and Sinan Aral
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